Well-posedness and stability for a nonlinear Euler-Bernoulli beam equation

被引：0

作者：

Deng, Panyu ^{[1
]}

Zheng, Jun ^{[1
,2
]}

Zhu, Guchuan ^{[2
]}

机构：

[1] Southwest Jiaotong Univ, Sch Math, Chengdu 611756, Sichuan, Peoples R China

[2] Polytech Montreal, Dept Elect Engn, 6079 POB,Stn Ctr Ville, Montreal, PQ H3T 1J4, Canada

来源：

COMMUNICATIONS IN ANALYSIS AND MECHANICS | 2024年 / 16卷 / 01期

基金：

中国国家自然科学基金; 加拿大自然科学与工程研究理事会;

关键词：

Euler-Bernoulli beam equation; input-to-state stability; integral input-to-state stability; boundary disturbance; Lyapunov method; TO-STATE STABILITY; LYAPUNOV FUNCTIONS; PARABOLIC PDES; FEEDBACK STABILIZATION; BOUNDARY DISTURBANCES; ISS; SYSTEMS; RESPECT;

D O I：

10.3934/cam.2024009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the well-posedness and stability for a nonlinear Euler-Bernoulli beam equation modeling railway track deflections in the framework of input-to-state stability (ISS) theory. More specifically, in the presence of both distributed in-domain and boundary disturbances, we prove first the existence and uniqueness of a classical solution by using the technique of lifting and the semigroup method, and then establish the L r -integral input-to-state stability estimate for the solution whenever r is an element of [2, +infinity] by constructing a suitable Lyapunov functional with the aid of Sobolev-like inequalities, which are used to deal with the boundary terms. We provide an extensive extension of relevant work presented in the existing literature.

引用

页码：193 / 216

页数：24

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